Question

if the critical angle for total internal reflection from a medium to vaccum is 30 degree . speed of light in medium is

Answer 1

we should know Snell's law
n1 sin I = n2 sin r
for critical angle the value of r becomes 90 degree
n1 / n2 = sin 90 / sin 30 = 2
also
n1/n2 = v2/v1
2 = 3 * 10^8 / velocity in medium
v= 1.5 * 10^8

Answer 2

In the medium, "speed of light" is $1.5 \times 10^8 \ m/s$

Explanation:

According to Snell's law, the ratio of sin I (sine of angle of incidence) and sin R (sine of angle of refraction) is equal to the ratio of v1 (velocity of light in medium 1) and v2 (velocity of light in medium 2). It is also equal to the reciprocal of the ratio of n1 ("refractive index" of medium 1) and n2 ("refractive index" of medium 2)

As the incident angle is always 90°;

Thus,

$\frac{n 1}{n 2}=\frac{\sin I}{\sin R}$

$\frac{n 1}{n 2}=\frac{\sin 90}{\sin 30}$

$\therefore \frac{n 1}{n 2}=2$

We also know that,

$\frac{n 1}{n 2} = \frac{v 2}{v 1}$

So,

$\frac{3 \times 10^{8}}{v 1}=2$

$\therefore v 1=\frac{3 \times 10^{8}}{2}$

$v 1=1.5 \times 10^{8} \ \mathrm{m} / \mathrm{s}$